REFERENCES
Samarskii, A.A., Teoriya raznostnykh skhem (Theory of Difference Schemes), Moscow, 1989.
Bakhvalov, N.S., Chislennye metody (Numerical Methods), Moscow, 1975.
Thomee, V., Lecture Notes in Mathematics, Berlin, 1984, vol. 1054.
Cockburn, B., Z. Angew. Math. Mech., 2003, vol. 83, no.11, pp. 731–754.
Zienkiewicz, O.C. and Zhu, J.Z., Int. J. Numer. Meth. Engrg., 1987, vol. 24, pp. 337–357.
Nochetto, R.H., Schmidt, A., and Verdi, C., Math. Comp., 1999, vol. 69, no.229, pp. 1–24.
Repin, S., Math. Comput., 2000, vol. 69, no.230, pp. 481–500.
Repin, S.I., Proceedings of the St. Petersburg Mathematical Society, 2002, vol. 9, pp. 143–171.
Neittaanmaki, P. and Repin, S., Reliable Methods for Mathematical Simulation. Error Control and a Posteriori Estimates, New York: Elsevier, 2004.
Repin, S., Rend. Mat. Lincei. Ser. 9, 2002, vol. 13, pp. 121–133.
Gaevskaya, A.V. and Repin, S.I., Mater. 5 vseros. sem. “Setochnye metody dlya kraevykh zadach i prilozheniya” (Proc. 5 Rus. Sem. “Grid Methods for Boundary Value Problems and Applications), Kazan, 2004, pp. 40–43.
Ladyzhenskaya, O.A., Kraevye zadachi matematicheskoi fiziki (Boundary Value Problems of Mathematical Physics), Moscow, 1973.
Ladyzhenskaya, O.A., Solonnikov, V.A., and Ural'tseva, N.N., Lineinye i kvazilineinye uravneniya parabolicheskogo tipa (Linear and Quasilinear Equations of Parabolic Type), Moscow, 1967.
Aintworth, M. and Oden, J.T., A Posteriori Error Estimation in Finite Element Analysis, New York, 2000.
Babuska, I. and Reinboldt, W.C., Int. J. Numer. Meth. Engrg., 1978, vol. 12, pp. 1597–1615.
Author information
Authors and Affiliations
Additional information
__________
Translated from Differentsial'nye Uravneniya, Vol. 41, No. 7, 2005, pp. 925–937.
Original Russian Text Copyright © 2005 by Gaevskaya, Repin.
Rights and permissions
About this article
Cite this article
Gaevskaya, A.V., Repin, S.I. A Posteriori Error Estimates for Approximate Solutions of Linear Parabolic Problems. Diff Equat 41, 970–983 (2005). https://doi.org/10.1007/s10625-005-0237-8
Received:
Issue Date:
DOI: https://doi.org/10.1007/s10625-005-0237-8